Evaluate each integral (a) (x² + x) dx (b) 6.** (secx + tanx)2 dx
Find the following integrals: SPENT Ox (26 - secx tanx) dx 4 evaluate the following definite integrals: b) 3 sinx Cos x V 1 + 3 sinx dx let u = 1 + 3 si nax
Verify the identity. 1- tanx 1-tan secx Factor the numerator (tanx-1)(1+tan %) (1 - tan²x) (1-tan?:) (1+tan :) (1 - tanºx) Simplify the fraction O 1+tanºx Use an identity to simplify the expression from the previous step 1-tan O sec? 0 1
Evaluate the integrals. Íx” dx = ſx=3 dx = (x-3) secx tan x dx = j(x?- Var)dx=
cos'x dx sin 3x dx 2. an 45 sin cos'xdx 4 sin'xcos'x dr 44 sin'x cos'r dr 6. sin'xcosx dx 8. Jo sin'x cosx dx fa-sin 2x)' dx sin x + cos x dx 10. 9 f sin'z dx cos'x sin'x d 12. 11 sin'x Vcosx dx 14. 13. cot'r sin'x dx 16. cos'x tan'xdx 15 dx sin x dx 18. 17 1-sin x cos x tan'x dx 20. tanx dx 19 sec'x d sec'x dx 22. 21 tan'x secxdx...
* 17. solve the integration (2 Points) Setan x+2 In(secx) dx = sec? x + c sec? x etanx + c tan x + c etan x + c
Find the general solution or particular solution of each the following DE's 1) (y-y2 tanx)dx + (2y+tanx)dy=0 2) (x2+y2+x)dx + xydy-0 i y(-1)-1 4) For the initial value problem y' + xy - xy? ex2 ; y(0)-1 Find the explicit solution if y>0 dy dae dy
Exercise 6. Double integral in rectangular coordinates (10 pts+10 pts) Let I = secx dydx. 2) By reversing the order of integration of I, we get: a. I = secx dxdy b. I = ('secx dxdy c. INSS secx dxdy d. I = So, secx dxdy
Exercise 6. Double integral in rectangular coordinates (10 pts+10 pts) Let I secx dydx. 2) By reversing the order of integration of I, we get: a. I = $ S secx dxdy b. 1= SS secx dxdy c. IESU secx dxdy d. 1 = secx dxdy
Exercise 6. Double integral in rectangular coordinates (10 pts+10 pts) Let I = SL, secx dydx. 2)By reversing the order of integration of I, we get: a. I = 16 secx dxdy b. I = foto secx dxdy c. 1 = 1secx dxdy d. 1 = SS, SS,' secx dxdy C. O d.